Slide rule



H. mmw.y SLIDE RULE. APPLICATION FILED MAR. I4. 1921- Fly. j.

Fly 2 -creased and UNITED STATES PATENT OFFICE.

To all wlwm z't may concern:

Be it known that I, HERMAN Rirow, a citizen of the vUnited States, residing in the city of Chicago, in the county of Cook and State of Illinois, have invented certain new and useful Improvements in Slide Rules, of which the following is a specification.

The present invention has relation to an improvement in that class of mathematical sliderules on both sides of the body and on both sides of the slide of said rules and known in' the art as Duplex slide-rules.`

The object of the present invention is to provide an improvement of the said`Du plex sliderules whereby the convenience and scope of operation of the rule is intheaccuracy of the rule greatly improved as hereinafter set forth.

attain these objects by a novel arrangement of logarithmic scales on both faces of a Duplex sliderule as illustrated in the accompanying drawing, in which,-

Fig. l is a plan perspective view of one face and one edge of the sliderule, to be hereinafter referred to as the upper face and upper ed and Fig. 2 is a p an perspective view of' the other face and of the remaining edge of the sliderule, to be hereinafter referred t0 as the lower face and lower edge of the said slidesule. y

Similar numerals and letters refer to simi- C, D, CL and T, as these are identical with logarithmic scales of sliderules now on the market, have been omitted from the drawing. These scales are known b those skilled in the art as 0, D, CI and T scales respective y.-

The integral parts ofthe improved sliderule are the sides 1 and 2, constituting the stock or body portion, the slide 3, which can be moved between the sides 1 and 2 and the runner (not shown in the drawing), which fits-snugly around the body portion and has two 'transparent faces with a hairline marked on each transparent face and can be moved freely from one end to the other of the rule. v

In Figs. 1 and 2 the slide 3 is shown moved toward the right between the sides 1 and 2 and the position of the slide is the same for both Fig. 1 and Fig. 2. The line F-F in the two figures shows the position of the hairlines of the runner.

Specication of Letters Patent. application ma :man 14, im.

provided with logarithmic scales 1 lar parts throughout the two views. Scales Patented Jan. 31, 1922. semi no. 451,949.

pon the upper and lower faces, Fi s. and 2 of the sliderule lo arithmic sca es are mar ed. The lines, mar ed G and H in t. e drawing, are the index lines of the lo rithmic sca es and are placed at the matiamatical beginning and at the mathematical end of each scale. The said scales extend beyond the lines G and H with the ob- ]ectof increasing the usefulness of the improved sliderule.

'The scale D on the upper face of the side 2 1s the usual lo arithmic scale 'shown on the wellknown annheim sliderules and known by those skilled in the art as the D scale of the Mannheim rule. With the exception of the marking for the number 25` the scale D is not shown in .detail on the drawing. The scale C on the upper face of the slide 3 indicated butnot shown indeta1l on the drawing is identical with and contiguous to scale Scale CI on the upper face of the slide 3, indicated but not shown in detail on the drawing is the reverse of scales C and D and its markings are the same distance from the right indexline as the corresponding markin of scales C and D are from the left indexline G. Scale CI is known by those skilled in the art as a verted scale.

Scale A-lO on the upper face of side 1 is the first half of a logarithmic scale of twice the len h of scale D,- and scale A-100 on t e upper face o ffside 2 is the other half of the same lo arithmic scale of double the length of sca e ,D, so 'that if the left indexline G of scale A-100 is laced over and coinciding with the ri ht inexlin'e H of scale JL- 10 we wo d obtain a logarithmic scale of twice the length of scale D. By this arrangement I provide what may conveniently be termed a folded logarithmic scale.

Scale I3-10 on the upper face of side 1 is the first third of a folded logarithmic scale of three times the length ofv scale D scale I3-100, on the lower faceV of side 2, is the' second third of the said scale of reciprocal or inthree times the length of scale D, and scale B-1000, on the lower face of side 1, is the last third of said scale of thrice the length of Vscale .D. If scales B-10, B-lOO and B-1000 are placed one beside the other so that vthe G line of B-100 coincides with the H line of B-lO and the G line of B-10GO coincides with the H line of B--100, the three scales will make together one long logarithmic scale of three times the length of scale D. l

Scale E`-10 on the upper face of slide 3 is identical with and contiguous to scale B-10, and scales E-lOO and IE-1000 on the lower face of slide 3 are identical with and contiguous to B100 and B-lOOO, respectively. These E scales constitute a thirdfolded scale arranged so that when the G and H lines of the slide 3 coincide with the G and H linesof the sides 1 and 2 all the markings on the E scales coincide with those on the B scales. In the usual Mannheim and Duplex scales the scale of squares is composed of two smalllogarithmic scales each of half the length o scale D and the scale of cubes is made up of three short scales each of one third the length of scale D. In my improved sliderule, as explained above, I use olded logarithmic scales of twice and three times the length of scale D cut into equal artsy each of the length of `scale 1).

herein lies both the improvement and the novelty of the sliderule as hereinafter set forth and explained.

The hairlines IL-F on the transparent faces of the runner, (not shown in the drawing),` are so marked that when one'of the hairlines F-F coincides with one of the G lines or H lines of the sides 1 or 2 the two hairlines coincide with all the other G lines or H lines, respectively, of sides 1 and 2.

rlhe scale T on the lower face (Fig. 2) of the slide 3, which scale is indicated but not shown in detail in the drawing, is for the purpose oftrigonometric calculations involving the tan ents of angles and is used in conjunction with scales C and D of the upper face. It is well known by those skilled in the'art as the tangents scale of the Mannheim rule. The scale S1 on 'the lower face of side 2 and the scale S2 on the lower face of side 1 are for the purpose of trigonometric calculations involving the sines of angles and are used in conjunction with the scales C and D of the upper face (Fig. l). The Scales S1 and S2 placed one beside the other with the G line of S2 coinciding with the H line of S1 make a folded sines scale similar to the well known sines scales of the sliderules now in use but of twice the length of scale Il In the usual sliderules the sines scale is used in conjunction with the scale ofl squares whereas4 in my improved sliderule the sines scales S1 and S2 are used in conjunction with the C and D scales. With the improved sliderule, therefore, trigonometric calculations involving the sines and tangents of angles can be done with the same logarithmic scales as are used for most ofthe multiplications and divisions, hence with much greater convenience and twice the accuracy obtained with the sliderules now o'n the market. .As the squares and cubes of numbers in vmy im roved sliderule are all found on the same and D scales all the usual computations can be done with the least loss of time on the one y roup of logarithmic scales 0, D and a much more convenient arrangement than that found on the sliderules on the market.

The scale Lonthe upper` edge of side -1 is similar to the wellknown scale of logarithms on the sliderules now in use and is obtained by uniformly subdividing a distance of three times the length of scale D into tenths, hundredths and smaller subdivisions and using the first third part of said uniform scale. It is placed along the upper edge of side 1 so that its indexline O is exactly at the edge of the runner when the hairline of the runner covers the G lines of sides 1 and 2. It is used in conjunction with the scales B-lO, I3-100 and 1S-1000 to determine the logarithms of the numbers on the B scales. The lefthand edge of the runner (not shown in the drawing) marks on the L scale the logarithm of the number under the F-F line on the i3- 10 scale. For the lo arithm of any number on the B-lOO or -1000 scales move the runner till the hairline covers the number and add to the reading of the L scale 0.33333 for B-100 numbers or 0.66667 for I3-1000 numbers. The logarithms so obtained are three times as accurate as those obtained with Mannheim sliderules on the market, of the same length as the improvedsliderul 1 On the remaining lower edge of side'2 `any ordinary inch or lcentimeter scale can Abe" printed or a table of engineering data made.

Multiplication and division can be done with the C, D and CI scales in exactly the s'ame way as with the scales on slide-rules now on the market. The use of the tangent or T scale in conjunction with the C, D and CI scales is also the same as with the usual sliderules. But in calculations in which a power is raised or a root extracted, in computations requiring great accuracy or involving the `sines of angles or the'tangents of angles of 5"l or less, the computations may be made Awith the sliderule I have invented not only far more conveniently but twice and even three times as accurately as correspondlng computations may be made with the Mannheim sliderules now on the market, as will now be set forth and explained in detail.

For any position of the runner the readin under the hair-line F-F on the scale Ig is the cube of each of the three readin under the hairline F-F on the scales 10, B-100 and B-1000, and the square of each of the readin s under the hairline F-F on the scales A-10 and A-100. This is readily seen if one imagines' the vthree B scales placed one beside the other as previously explained to make one long logarithmic scale of three` times the length of scale D and then the scale D placed under the three parts, and repeated three times with the G and H lines corresponding as before. This would obtain the same relation between the three scales D and the long combined B scale as between the cube scale` and the D scale of the sliderules now on the market. similar combining of the two A scales into one longl scale op osite two D scales will show the same re ation as between the D and A scales of the Mannheim rule.

Hence to obtain the root of a number set the runner so that the hair line F-F is over the number on the scale D and read oi the cube roots and the square roots on B17 A der the hairline F-F. Use the I3- 10 scale for cuberoots of numbers between 1 'and 10, multiplied or divided by any power of 1000. Use B-100 scale for the cube root of any number between 10. and 100., multiplied or divided by any power of 1000. Use the B-l000 scale for the cube root of' any number between 100 and 1000, multiplied or divided by any power of a 1000.W Use the A-lO scale for the square root of any number between 1 and 10, multiplied or divided by any power of 100. Use the A-lOO scale for the square root of an number between 10 and 100, multiplied or divided by any power of 100. The cube root or squareroot depends, therefore as usual,

` on the position of the decimal point in the A on a scale whose power, but, though there are three possible cube roots and two possible square roots of every ii re, all five of these roots can be obtaine with one setting of the runner. In the sliderules on the market three settin of the runner are necessary for the three possible cube roots of a figure and two 'settings for the two `square roots. As the cube root is obtained on my improved sliderule three parts combined are three times as long as the scale D the accuracy of the cube root so obtained is three times that obtained on the D scale of the sliderules now on the market of the same length as the improved sliderule. For a similar reason the accuracy of the squareroots obtained on my improved sliderule is the D scale.

scales, respectively, all uny cated and twice as eat as that obtained on the sliderules of t e same length now on the market, with the exception of the Fabre or Nestler sliderules made in Europe and using the A-lO and A-100 scales.

To obtain the cube of a number set the runner with the hairline F-F over the number on one of the B scales and read the answer under the hairline F-F on the D scale.

As the D scale is three times as long as the cube scale of the sliderules on the market my improved sliderule gives the cubes three times as accurately as the sliderules of the same length now sold.

To obtain the square of a number set the runner with the hairline F-F over the number on the A-10 or A-lOO scale and read the answer under the hairline on The same accuracy is ob- Nestler sliderules made in urope, but my improved sliderule 'ves the squares on the very convenient scale whereas the Nestler rules give the squares alongthe edges away from the slide, and has no C scale, and the Mannheim rules give the squares along the Scale of Squares which are half as accurate as, the D scale.

Since the numbers on the D scale represent the squares of those on the scales and the cubes of the numbers on the B scales, it follows that the B scale numbers are the two-thirds (2 /3) powers of the A scale numbers and. the latter are the threehalves (3 /2) owers of the numbers on the B scales. (liie setting of the runner gives at once the three possible two-thirds powers and the two ossible three-halves powers that correspon the location of the decimal in the original figure determining the choice of the correct root.

In the drawing the hairline F-F covers the numbers givenvbelow on the scales indithese illustrate the manner in which the improved sliderule gives the roots and powers.

tained 'with the plying and dividing with the B and E scales is identical with the same operation carried on with the C and D scales except that any one of the three B scales is used with any one of the three E scales without regard to the contiguity ofthe scales to each other. Thus with the help of the two hairlines on the transparent faces of the'runner any number on the B-10 scale can be divided by any number on the IE-100 scale although the latter scale is not even on the same side of the rule as the 5B-10 scale. The hairline of the runner is set over the number on the B-10 scale and the slide is moved till the divisor on F -F of the lower face of the runner. The answer must be picked out of three figures on the B scales found opposite the indexlines G or H of the slide. This choice is made either by a preliminary operation of the C and D scales or by a mental calculation.

Thus the division 13.57 /2.658::5.106 is done on the improved sliderule by moving the runner until the hairline F-F covers the number 13.57 on the B lO scale, turnv ing the rule over to the lower face (Fig. 2.)

and moving the slide 3 until the number 2.658 on the E--100 scale is directly under the hairline F-F. The answer is read on the Bl000 scale opposite the indexline G of the slide after the choice among the the three numbers on the B scales opposite the G lines of the slide has been decided by the vmental computation that the answer must be somewhere between 5 and 6. Figures 1 and 2 of the drawing show the setting of the slide and ofthe hairlines =FF for the above division and for the folheim D scale on one face of the stock, a

lowing computations The combination of double-length and triple-length logarithmic scales with the D scale of the Mannheim rule gives my improved sliderule the greatest convenience in working With cubes and cuberoots, squares and squareroots, three-halves and two-thirds powers, increasing the accuracy of these operations two-fold and threefold; makes it possible to do all the usual computations with the convenient C D and Cl scales; and makes my improved slide rule a very handy instrument for calculations requiring normal accuracy and at the same time a rule with which computations can be made with the same degree of accuracy as with Mannheim sliderules of three times the length of my improved sliderule. These advantages should serve to recommend it to engineers and calculators.

I do not limit myself to the actual arrangement of scales shown in thel drawing so long as the broad description heretofore given 1s complied with, as my invention includes such modifications as would occur to those skilled in theart. Furthermore, I do not limit myself to the use of folded scales made up of parts aggregating only two or three times the graduated length of the rule as they may comprise .a sufficient number of parts to make up any desired aggregate length.

I claim as new and desire to secure as Letters Patent 1. A slide rule comprisin a stock havin guides and a slide, Mann eim D and scales of the graduated length of the rule carried by the stock and slide respectively, and folded logarithmic scales carried bythe stock and slide respectively, each of said folded scales consisting of a plurality of consecutively subdivided parts each of the graduated length of the rule and having index lines at their mathematical beginning and end coincident with the index lines of said D and C scales respectively.

2. A slide rule comprising a stock having guides and a slide adapted to be moved longitudinally between said guides, a Mannheim D scale on one face of the stock, a

Mannheim C scale on the slide adjacent to l the D scale, and folded lo arithmic scales carried by the stock and slide respectively, each of said folded scales being composed 0f two parallel parts of equal length ruled consecutively to indicate the square roots of correlative numbers of the D scale, each of said parts having index lines coincident with the index lines of the D scale.

3. A slide rule comprising a stock having guides and a slide adapted to be moved longitudinally between said guides, a Malm- Mannheim C scale on the slide adjacent to the D scale, and folded logarithmic scales carried by the stock and slide,'each of said folded scales being composed of three par- -allel parts of equal length ruled consecutively to indicate the cube roots of correlative numbers of the D scale, each of said parts having index lines coincident with the index lines of the D scale.

l. A slide rule comprising a stock having guides and a slide adapted -to be moved longitudinally between said guides, a Mannheim D scale on the upper face of the stock adjacent to the lower margin of the slide, a Mannheim C scale on theupper face of the slidev adjacent to the D scale, a folded logarithmic Iscale .carried by the stock parallel with the slide, the latter scale being com-V posed of three parallel parts of equal length ruled'consecutively to indicate the cube roots ofcorrelative number of the Dscale, one of said parts being arranged on the upper sur face of the stock adjacent to the upper margin of the slide. and others of said parts being arranged on the under surface of the.

stock adjacent to the upper and lower margins of the slide respectively, and a scale on the upper and under surface of the slide, the latter scale being composed of three parts placed adjacent respectively to the upper and lower margins of the slide, and identical respectively with adjacent parts of the folded logarithmic scale on the upper and under surface of the stock, each of said parts having index lines coincident with the index lines of the D scale.

5. A slide rule comprising a stock havin uides and a slide adapted to be move ongitudinally between said guides, a Mannheim D scale on one face of the stock adjacent to the lower` margin of the slide, a Mannheim C scale on the corresponding face of the slide adjacentto the D scale, folded logarithmic scales carried by the stock and slide, each of said folded scales bein composed of two parallel parts of equal ength ruled consecutively to indicate the square roots of correlative numbers of the D scale, and a sine scale carried by the stock, said sine scale being composedof a plurality of consecutively subdivided parts each having index lines coincident respectiely with the index lines of the D scale.

In witness whereof I sign my name in the presence of two witnesses.

Henman RITOW.

Witnesses:

BERNARDINI BERNARD,

LvILLE F. HORINE. 

